How do I find the rotation matrix to transform from the global coordinate frame $(x,y,z)$ to a rotated local coordinate frame $(x',y',z')$, given I have the orthonormal basis vectors of the local coordinate frame?
For example; I have a coordinate frame whose basis vectors are $$x' = (0.5774\;;\; 0.5774\;;\;0.5774) $$$$y' = (-0.8165\;;\; 0.4082\;;\;0.4082) $$$$z' = (0\;;\; -0.7071\;;\;0.7071) $$
How do find $R$ such that $$R\begin{pmatrix} 1 \\0\\0\end{pmatrix} = \begin{pmatrix} 0.5774 \\0.5774\\0.5774\end{pmatrix}$$